Question

Моторная лодка, обладающая скоростью движения20 км/ч, прошла расстояние между двумя пунктами по реке туда и обратно не останавливаясь, за 6 ч 15 мин. Определить скорость течения реки, если расстояние между пунктами равно60 км.

Answer 1

Пусть х км/час=- скорость течения
20+х км/час=скорость по течению
20-х км/час =скорость против течения
6 час 15 мин=6 ц 15\60=6,25 время 
60/(20+х) + 60/(20-х) = 6.25
1200-60х+1200+60х=6,25*(20²-х²)
2400=6,25*(400-х²)
2400=2500-6,25х²
6,25х²=100
х²=16
х=4

ответ 4 км/час скорость течения реки

Answer 2

Problem Analysis

We are given the following information: - The motorboat travels at a speed of 20 km/h. - The motorboat travels a distance of 60 km between two points on the river, both ways, without stopping. - The total time taken for the round trip is 6 hours and 15 minutes, which is equivalent to 6.25 hours.

We need to determine the speed of the river's current.

Solution

Let's assume the speed of the river's current is x km/h.

When the motorboat is traveling downstream (with the current), its effective speed is increased by the speed of the current. Therefore, the speed of the motorboat downstream is 20 + x km/h.

When the motorboat is traveling upstream (against the current), its effective speed is decreased by the speed of the current. Therefore, the speed of the motorboat upstream is 20 - x km/h.

We can use the formula distance = speed × time to calculate the time taken for each leg of the journey.

The time taken to travel downstream is given by: time_downstream = distance / (20 + x)

The time taken to travel upstream is given by: time_upstream = distance / (20 - x)

Since the total time taken for the round trip is 6.25 hours, we can write the equation: time_downstream + time_upstream = 6.25

Substituting the values, we get: distance / (20 + x) + distance / (20 - x) = 6.25

We know that the distance between the two points is 60 km, so we can substitute that value as well: 60 / (20 + x) + 60 / (20 - x) = 6.25

Now, we can solve this equation to find the value of x, which represents the speed of the river's current.

Calculation

Let's solve the equation 60 / (20 + x) + 60 / (20 - x) = 6.25 to find the value of x.

Using the search results, we can see that there are no relevant snippets that provide a direct solution to this equation. Therefore, we need to solve it algebraically.

To solve the equation, we can multiply both sides by the common denominator, which is (20 + x)(20 - x).

After simplifying the equation, we get: 60(20 - x) + 60(20 + x) = 6.25(20 + x)(20 - x)

Expanding and simplifying further, we get: 1200 - 60x + 1200 + 60x = 6.25(400 - x^2)

Simplifying the equation, we get: 2400 = 2500 - 6.25x^2

Rearranging the equation, we get: 6.25x^2 = 100

Dividing both sides by 6.25, we get: x^2 = 16

Taking the square root of both sides, we get: x = ±4

Since the speed of the river's current cannot be negative, we can conclude that the speed of the river's current is 4 km/h.

Answer

Therefore, the speed of the river's current is 4 km/h.